A grinding wheel having two each other opposing and away from each other pre-tensioned grinding discs arranged on a shaft with crosswise arranged free protruding fingers is previously known from U.S. Pat. No. 989,692. This grinding wheel is not intended to be brought into a driven rotation, as is the grinding wheel of the present invention, and requires a manual forth and back movement of the blade of a knife in the notch that is formed between the stationary arranged fingers. A disadvantage of this grinding wheel is the limited use of the abrasive surface of the grinding disc, which results from that only a narrow peripheral region is active for treatment of the edge. Another disadvantage is the risk that an edge having a sharp, unprotected corner getting caught by the grinding wheel upon insertion of the edge into the grinding wheel. This disadvantage can be seen as less important in connection with the stationary grinding wheel of U.S. Pat. No. 989.692, but is of great importance in connection with a grinding wheel which is driven to rotate at speeds of around 3000 rpm. Another disadvantage with this prior-art grinding wheel is that the treated edge, as viewed in a cross-section, is formed with a thin edge with concave-shaped sides, whereby the edge becomes thin and fragile and sensitive to deformation and wear. Furthermore, the efficiency of this grinding wheel is suffering from the fact that the operator needs to turn the grinding wheel into a non-used area before the grinding takes place.